2002/04/23 by Tom Leinster · 1 citation
Mathematics · #math.CT #msc:18D20 #msc:18D05 #msc:18D50 #msc:18D10
published as Journal of Pure and Applied Algebra 168 (2002), 391-406 · 18 pages; written 1999
arxiv created 2002/04/23 · arxiv updated 2009/11/30
We define the phrase `category enriched in an fc-multicategory' and explore some examples. An fc-multicategory is a very general kind of 2-dimensional structure, special cases of which are double categories, bicategories, monoidal categories and ordinary multicategories. Enrichment in an fc-multicategory extends the (more or less well-known) theories of enrichment in a monoidal category, in a bicategory, and in a multicategory. Moreover, fc-multicategories provide a natural setting for the bimodules construction, traditionally performed on suitably cocomplete bicategories. Although this paper is elementary and self-contained, we also explain why, from one point of view, fc-multicategories are the natural structures in which to enrich categories.